Theorem uneq12i 2182

Description: Equality inference for union of two classes. (The proof was shortened by Eric Schmidt, 26-Jan-2007.)

Hypotheses

Ref	Expression
uneq1i.1	|- A = B
uneq12i.2	|- C = D

Assertion

Ref	Expression
uneq12i	|- (A u. C) = (B u. D)

Proof of Theorem uneq12i

Step	Hyp	Ref	Expression
1		uneq1i.1	. 2 |- A = B
2		uneq12i.2	. 2 |- C = D
3		uneq12 2179	. 2 |- ((A = B /\ C = D) -> (A u. C) = (B u. D))
4	1, 2, 3	mp2an 697	1 |- (A u. C) = (B u. D)

Syntax hints:   = wceq 956   u. cun 2045

This theorem is referenced by:  indir 2253  difundir 2258  difindi 2259  symdif1 2265  unrab 2270  iunun 2613  unopab 2679  xpundi 3225  xpundir 3226  xpun 3227  resundi 3378  resundir 3379  rnun 3457  imaun 3460  imaun2 3461  unidmrn 3516  fvsnun2 3796  df2o2 4141  sbthlem5 4451  rankpr 4692  rankelun 4707  cbvsum 6986  acdc2lem2 7489  acdc5lem2 7492  ruclem6 7515

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-un 2050

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